Babies as Human Capital in an OLG model

I'm trolling Elizabeth Breunig. Because she said that "Human capital is one of the more odious terms in the capitalist lexicon". And I like the term "human capital", because I think it helps us think more clearly about investment in training and education.

Are new-born babies "human capital"? My first thought was that they possess no human capital, because they haven't invested in learning anything yet, so it was an abuse of the concept to say that babies are human capital.

Then I remembered "Lark Rise to Candleford", (HT Frances), a memoir of 19th century girlhood in a poor English village. Only one couple in the village had any savings. They were saving for their pension. They were the only childless couple in the village. All the other couples had children, who were costly to feed and clothe, but would support them when they were too old and sick to work. Their children were their pension plans.

At the individual level it might no longer be true that we expect our own children to support us in our retirement. But at the aggregate level it is still true. If nobody has any children, who will produce the goods and services we will consume when we are retired? Unless we can store consumption goods, or invest in building robots that don't need human labour to produce goods.

Think about a OverLapping Generations model with three generations: kids, parents, and grandparents. Only the parents work.

There is a Cobb-Douglas technology in which labour L and non-human capital K produce output, which can be either consumed C or invested I in creating more non-human capital.

C + I = La Kb where a+b=1 and dK/dt = I - dK where d is the depreciation rate, usual stuff.

A Barro-Ricardo version of the model assumes intergenerational altruism, where each individual maximises the sum of the utilities of all three generations. But dynasties are selfish, in the sense that individuals care only about themselves, their own kids, and their own parents.

If all dynasties are identical, the competitive equilibrium will duplicate the social planner's problem. You would not need to introduce Samuelsonian "money" into the model to ensure dynamic efficiency, because retired grandparents will support and be supported by their middle-aged children anyway, with gifts flowing in either direction, depending on the parameters in the model. There are no externalities between dynasties.

What happens if we relax the assumption of intergenerational altruism?

If the whole population stops having kids, because they don't care for their kids, and they know their kids won't care for them, they are in a collective pickle. They can still invest in non-human capital for their retirement, but there won't be any middle-aged workers to add their labour to that capital. So the rate of return on their investment will be minus the depreciation rate d. And that is the most favourable assumption, because I am assuming the investment process is fully reversible, so that machines can be converted back into consumption goods at zero cost.

That is an extreme case, of course, and a population like that will die out anyway. But it illustrates the point that there is an externality. My having kids will increase the labour supply when I am retired, which will increase the rate of return on my investment in non-human capital. But I can't force my kids to work with my machines; they will work with your machines too, and raise the rate of return on your investment. And if the population is large, almost none of the benefits will flow to me. Those who are selfish would agree to a social compact where they will all have more kids to work on each others' machines when they are retired, to raise each others' rate of return on their investment in non-human capital.

Are they treating their own kids as a means to an end? Yes. And in part, it was ever thus, in the age before pension plans. And it's still true today, in aggregate. My kids are part of your pension plan, and your kids are part of my pension plan.

But (I think this is true in the model) those who are Barro-Ricardian, and who want to have kids anyway, and can have kids anyway, might not care about them others who don't have kids. And they will die out anyway. But it's tough on the people who can't have kids, for whatever reason, if nobody else does.

I'm not 100% sure I've got my head fully around this idea yet. But don't say I'm odious for thinking about these things. They matter for human welfare, and they might matter a lot. And we need to think about them clearly.

[Update. If we add a fixed stock of land to the model, as perhaps we should, then the population level matters too. Without land, and with constant returns to scale, only the population growth rate matters.]

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I think your first thoughts were correct: it is an abuse of the concept to say that babies are human capital. But in fairness to Elizabeth Breunig, she's responding to Jim Pethokoukis and Pascal-Emmanuel Gobry, both of whom abuse the concept in just that way.

However, since you yourself use the term "investment" in a highly expansive way, here's how to solve the problem of kids who won't support you in your old age. "Invest" in a religious doctrine which says Honour thy father and thy mother. Then their belief that they will roast in Hell if they don't keep you in style in your dotage becomes part of your "capital", a kind of Divine Capital.

Expand a concept far enough and all meaning evaporates. Political capital, diplomatic capital, anything goes. But here's a question which has long puzzled me: just what did Joan Robinson mean by saying that "capital" is not what capital is called, it's what its name is called?

Kevin: I'm not sure what Joan Robinson meant, but let me guess, by giving my own view, so saying what she *should* have meant.

I would say that capital is not really a thing; it's just the name we give to a production process where time matters, because inputs and outputs occur at (perhaps multiple) different times. And time is a vector, and it's generally impossible to convert a vector into a scalar. (Plus it's a matrix if there are different goods at different times.) Now if we were all perfectly patient, and didn't care about when we consumed, we could ignore time, and we wouldn't need the word "capital". But we do care, so goods at different times have different relative prices, just as apples and bananas have different relative prices, because we care about which one we are eating, as well as when we eat them.

And once you think about "capital" as just the name we give to the time-structure of production, then brain surgeons are just as much "capital" as Joan Robinson's broomsticks and blast furnaces. The costs come first; the benefits come later.

BTW Kevin: you are to blame/credit for me writing this post. I don't think I would have clicked through to Elizabeth Breunig's article if you hadn't said I had gone into battle with her unprepared. I was just battling Paul Krugman, but you successfully trolled me. (God I hate that term "troll", and I should stop using it. I think this is the first time I have used it in a post, and I will try not to use it again. "Concern troll" is even worse.)

From the perspective of a non-economist, one of the oddest things about reading most economics blogs is the extent to which the definition of words and phrases is such a big issue. In this case, “human capital”. I don’t think that you can talk about “human capital” without the equally dreaded word “investment”. Here are three examples of investment (a process) creating capital (an output).

First, a construction company takes some bricks and other materials. It adds energy from a bunch of machines and further energy and skills from a bunch of labourers. It produces output of an increased stock of houses. The investment process creates capital.

Second, a food manufacturer takes some flour and other materials. It adds energy from a bunch of machines and further energy and skills from a bunch of labourers. It produces output of an increased stock of pizza. The investment process again creates capital.

Third, a university takes some school leavers and other materials such as whiteboards. It adds energy and skills from a bunch of professors. It produces output of an increased stock of educated students (and an increased stock of intellectual property). This is directly analogous to the earlier examples. If the stocks of houses and pizzas are capital then so are the stocks of educated students and IP.

In summary, this investment creates something new.

After this we buy and sell all of the things above. However, buying and selling always go together and have equal and opposite effects. For example, if my construction company sells a house to a holiday rental company, the holiday company invests in the house but only because the construction company dis-invests in the house. Similarly, the holiday company pays for the house by dis-saving and the construction company receives payment and then saves the same amount. Buying and selling always occur together so the related investing and dis-investing, and the related saving and dis-saving, also go together.

Similarly, when the food manufacturer sells a pizza to a consumer, the manufacturer’s stock of pizza decreases by one and the consumer’s stock of pizza increases by one. The consumer then eats the pizza but that is a separate step which reduces the consumer’s stock of pizza by one.

Similarly, when an employer hires an educated ex-student, he gets the ex-student including the skills produced by the investment from the university. The only real difference to the other examples is that it is the student (the output of the university process) who sells (or, more accurately, rents) himself to the employer whereas, in the other examples, it was the business which did the selling.

When we say that we (or our pension funds) are investing for our retirement, we are just buying shares or government bonds etc which means that someone else is selling them. If we are investing then the seller is disinvesting. When we retire we will want income from these investments, and we will want to rent holiday homes and buy pizzas. However, those things depend on the activities of construction companies, holiday rental companies and food manufacturers, and the skilled staff educated by the universities. Hence we are dependent on continued value adding investment which creates new things.

Similarly, in the olden days, a farmer might have invested in educating his family in how to run a farm so that, in his old age, the farm could be run without him. His investment increased the stock of knowledgeable farmers.

Jamie: I am in agreement with your examples and the conclusions you draw from them. (Except, if the pizza has to be eaten immediately, it's not capital, but you are assuming they can be stored for at least a bit, I think, so it is capital.)

Nick: Yes, the stock of pizza is only capital until it is eaten. However, what I am saying is that assets, consumables and people skills are all capital. They are just used for different purposes and they all have different active time spans. A pizza is consumed after only a few days so we think of it as a consumption good from the perspective of the person who buys it and eats it. A house may last for centuries so we think of it as an asset. A skilled ex-student may have a career of 40 years so that seems like an asset too.

I agree that moving things around is important in terms of distributing the capital and galvanising the system. However, it is the production of the capital that is most important. Otherwise there is nothing to move around but whatever we can find lying around. That's the problem for pensioners. If no-one is producing pizza then pensioners can't eat pizza no matter how much they have invested or saved for their retirement.

Can we get this three-generation model to work without altruism but with red and green money? Assume (red+green) can be produced ex nihilo, but no-default and no-bequest conditions mean that at death an agent must balance to zero. This models an altruistic or social obligation as a legal one.

The schematic is that children have no income, so they create red money + green money for consumption; the consumption goods (may) partially determine their productivity as adults. Adults earn green money on the market, which is spent on current-period consumption and saved for old-age. The elderly retire any red money they still hold on to, and then they spend the remainder.

Most of the world (i.e. China + India + most of Africa) still sees children as a pension plan.

In Singapore, the practice is part of the culture. For those who dont like it, the practice is legally mandated - though in practice it's hard to force (parents don't sue their children, even dead beat children).

I think Jamie and Nick express it well. We do invest into children and we (as a society) do get a return. That sounds like 'capital'. Sports teams do account for humans as assets and some other companies think of humans that way (or some of the humans at least).

Two hundre hears ago, people would have had no trouble thinking of humans and human capital as capital assets - slaves. Granted, that particular asset class got wiped off the balance sheet in most parts of the world by the end of the 19th century. Still, that's an example that makes the equation human capital=capital explicit.

Majro: very good question. I was thinking about introducing negatively-valued money into the model, but I thought it would freak people out even more. Parents would give their kids red money. Grandparents give their adult kids green money. I'm not sure if there would be externalities in equilibruium.

Can't find the link to my old post on "negatively-valued (red) money".

Would they? Without altruism, I'd think that the old generation would sell its capital to the younger generation, retire any red money on hand, and then spend the rest of their green money in Hawai'i. Consumption-smoothing would ensure that there wouldn't be too much green money left for Hawai'i.

We may also get different results if parents decide how much red money to give to children, compared to if children could decide for themselves. Selfish parents would only try to optimize current+old consumption, whereas selfish children would care about all three periods.

> Can't find the link to my old post on "negatively-valued (red) money".

First, people who don’t like the term “human capital” don’t like it because it suggests ownership. However, that misses the point. Capital is about value. A trained doctor is more valuable than an untrained one. It also misses the point because, in ownership terms, we all own our own capital. It is the trained doctor who makes use of his own capital value to earn money by curing patients. (It would also be the trained doctor who decided to waste his human capital by accepting a job cleaning the hospital rather than curing patients).

Second, by chance, last time I posted on this blog was a long time ago on one of the red-green money threads. This would be my take.

It is worth going to the bank to obtain equal parts red and green money if the green money can be used to add sufficient capital value.

For example, suppose a young person thinks that they can increase their capital value by attending university and training to become a doctor. The increased capital value will allow them to spend their lives curing patients rather than cleaning hospitals.

In that case they may obtain equal and opposite amounts of red and green money from the bank. They use the green money for university fees and for pizza which allows them to study for a few years until they qualify.

After qualifying, the young person has no green money left, only red money. However, as the green money has allowed them to invest in their own personal capital, they can now take a job curing patients and earning lots of green money. This allows them to get rid of their red money and then live happily accumulating green money until they retire.

Nick: "And I vaguely remember it's still the law in Germany, that kids must support desitute parents?" No need to go that far. As a Québec resident, even of the other solitude persuasion, it's good to know:
Civil code of Québec art. 585
Art. 585. Married or civil union spouses, and relatives in the direct line in the first degree, owe each other support.
Courts enforce this obligation. Formerly covered grand-parents and grand-children but eliminated in 1994.
http://www.justice.gouv.qc.ca/english/publications/generale/extraits-codes-a.htm

Thanks. That raises the question of what is an economist I have been reading economics blogs by well-known economics professors, spanning both mainstream and heterodox, for several years. I’m sure that I have spent more time on this than many students who have studied economics at university for, say, a couple of years. I also spent many years working on operational problems in business and government. Many of these are relevant to economics although no-one involved in those problems was an economist. Does that make me an economist? I don’t know? Probably not. No-one in the real world would think of me as an economist even though I know more about economics than any of my friends and family.

We would not survive as a species if we did not obtain great utility from raising offspring, which is why we continue to raise offspring long after children stopped being a form of capital.

The slavery model is a good one. Early societies did view children as wealth, but they invested relatively little in those children compared to modern societies (no college tuition here and free support was provided only for a few years) and made those kids work from a very young age. The relationship between parent and child was closer to what we would view as a property/owner relationship than what we are used to with children in the present. E.g. children were required to obey their parents, parents could hurt their children, parents could take their children's property, control their children's non-work social life, etc.

In the present, even the most neglectful parent would be better off financially investing the proceeds spent on child raising into stocks and letting those returns accumulate for 40 years rather than raising the kids and hoping that they would help out with the parent's retirement. Relying on retirement-only income doesn't work very well because the kids are having their own kids at that time. This human capital view only works if the children begin providing income to the parents shortly after being born. Then their children provide income to them and your children provide income to you.

Jamie:" it is the production of the capital that is most important. Otherwise there is nothing to move around but whatever we can find lying around. That's the problem for pensioners. If no-one is producing pizza then pensioners can't eat pizza no matter how much they have invested or saved for their retirement."
Years ago, there was serious discussion in Québec about woman staying home accumulating credit toward the RRQ system (equivalent to CPP). It was shot down by femisit claiming that it would be bad for women. In the meanwhile, fertility is co0ntinuing to crash and so are the vialbility of pension plans, whatever the actuaries might say.

Sorry, I don’t get why having a baby creates an externality.
Yes, having one more child adds to the future labor supply and increases future output. But in a competitive market, my kid will get all of the additional output. The income of non-human capital owners doesn't increase, there's no externality. Even if there’s imperfect competition in the labor market, my kid will still get most of the additional output while the rest is spread over millions of non-human capital owners, so the externality will be tiny.
And if you think increasing the future labor supply (=having a baby) creates an external benefit to society, do you think increasing present labor supply (=work more hours) does the same? If not, where’s the difference? If yes, do you think labor supply is inefficiently low in unregulated markets in general?

D: more future labour changes the future distribution of income, so wages fall and rents on capital increase. From the POV of the current cohort of middle-aged, that's a (pecuniary) externality. Just like capitalists wanting more immigration.

Remember that the middle-aged will be capitalists next period. With a Cobb-Douglas technology (for example), capital's share remains fixed, but if the labour supply increases, the capitalists get the same percentage share of a bigger aggregate output.

In this model capital has value bc of the value of future consumption goods it can produce. But the consumers of those goods have become capital as well, and so the consumption is investment (and maintenance). Thus the value of the consumption goods is the value they add to the human capital's future ability to produce consumption goods whose value is defined by the value they add to be productive capacity of future human capital ....
I don't know, it's a little un satisfying to me. With Humans as distinctly their own thing, consumption goods get their value from Humans and capital has value for its future ability to produce consumption goods. How valuable a future string of consumption goods is likely to be depends heavily on the future number of humans. Meanwhile, investing in a future human makes more and more sense the fewer future humans you expect to be around (and thus the lower value of current capital goods).
We can collapse Humans into Capital, but it seems to make things less clear to me.

Nick Y: in this model, the middle-aged invest in capital because they want to consume in future when they are retired. But that capital (by assumption) requires labour to produce those consumption goods. If the middle-aged could invest in robots, that didn't require human labour (if I changed the production function to C+I=L+K, where K is robots) then it would be a very different model.

Human capital is one of the more odious terms in the capitalist lexicon. The phrase advances a couple of key confusions: First, that human value arises from an ability to produce wealth;

Nick says:

If nobody has any children, who will produce the goods and services we will consume when we are retired? Unless we can store consumption goods, or invest in building robots that don't need human labour to produce goods.

She's saying that your sentence implies the opposing conclusion that if such goods or machines were invented, then humans would stop having children - that there is no ulterior motive (in aggregate or individually) for having children other than feeding a perpetual pension scheme.

...second, that there is no distinction between labor (the work that humans do) and capital (sources of wealth that passively generate income).

The point here seems to be about distinguishing between wealth generation (by generation 2 in your model)through active and through passive means. If humans can be considered as incorporating capital, then that distinction is blurred as human capital cannot be employed passively. It can only be actively employed or not employed at all.

Fair point, I guess bu also not fundamentally at odds with the view you express here, I'd say. Just a matter of overlapping terminology.

Nick, as always, you cut to the essence of the issue (that's a weirdly mixed metaphor) - precise, clear, insightful.

Somewhat off topic - I find it mildly entertaining the way that people either will embrace or critique human capital depending upon the implications of human capital theory in that particular situation. Take, for example, grading and grade inflation. I know some politically correct types - ones who see capitalist economics as generally a bad thing - who don't hesitate to justify giving all of their students As and Bs on the grounds that "everyone in the class achieved the course learning outcomes" - very much an education-teaches-you-useful-stuff human capital type perspective. Of course someone like me, who is highly skeptical of human capital theory, would say - no, this is all about signalling, the value of education comes from the fact that some people succeed, some people fail, and thus the ability to succeed is a useful signal of innate ability/productivity.

You'd be witnessing a materialist Marxist shooting her own foot. I don't know Bruenig, but the first sentence I quoted felt decidedly non-materialist. Value being the non-materialist, moral term, as opposed to (material) wealth.

The term labour itself also isn't helpful, not least because it's historically laden. A more neutral term might be effort? Nice and protestant. But, and I take this to be your main point, it's also crude and needs to be refined. The concept of human capital being one way to do so because it manages to capture the implications of effort over the course of (a life)time. And to appease the lefties, thanks to Bourdieu the terms social, cultural and symbolic capital are well known categories in sociology.

But the question remains, which human trait or input merits the outcome we call wealth? And I don't see why the division into effort / no effort is not a valid starting point for an inquiry.

Frances: thanks! It does tie on with some of your past posts (not just the Lark Rise to Candleford one).

Yep, I'm getting a bit annoyed at how the term "human capital" is becoming a political football. It's a concept that (some/most) economists find useful for thinking about investment in people's abilities. Those of us in the education business have a vested interest in opposing the signalling theory. But I think it must be partly true, though a lot depends on the particular things being taught. Driver's ed., for example, looks like human capital to me. Dentistry too, I would think, though maybe a bit of barriers to entry as well.

One thing I've been puzzling over, with my model, is whether introducing sex would change anything. If I replace "parents" with "mothers and fathers", the dynasties would keep crossing each other, but I'm not sure if anything else would change. The mother would care about her parents, and the father about his, for example, but if you model the couple as a cooperative equilibrium, I think things would come out much the same. But I'm not sure. I'm racking my brain to remember something relevant I read recently, without any luck. Might have been something of yours?

Oliver: yep, she seemed to be using the words "human value" in two senses. Some poor UK politician got into trouble similarly recently, by saying something like disabled workers weren't worth much. But you have to try hard to misunderstand what he meant.

"A more neutral term might be effort?"

Yep, but that's problematic too. A task might be effortless for one person, but require a lot of effort for another, even if hours worked is the same. Did one do less labour than the other? You can tie Marxists in knots with this sort of stuff. They end up defining quality of labour by wage paid, which is circular. My late colleague Eddie West did a paper on this once.

"But the question remains, which human trait or input merits the outcome we call wealth? And I don't see why the division into effort / no effort is not a valid starting point for an inquiry."

Take a top baseball player and a top cricket player. If people like watching baseball more than cricket, the first will become wealthier than the second. And both might be willing to play for free, if nobody liked watching, simply because they enjoyed playing, and didn't think of it as effort or work.

"If we add a fixed stock of land to the model, as perhaps we should, then the population level matters too. Without land, and with constant returns to scale, only the population growth rate matters"

Can you clarify the importance of the distinction here? I'm pretty sure that with or without land, but endogenous fertility choice, population growth goes to zero and so does growth in aggregate output. There might be some parameters restrictions there so you don't get the weird case where L goes to zero and per capita income goes to infinity and these might be different with or without land but it does seem very important.

notsneaky: "I'm pretty sure that with or without land, but endogenous fertility choice, population growth goes to zero and so does growth in aggregate output."

I'm not sure that's right. There are two effects: If parents have twice as many kids, that's twice as much total kids' utility; but the parents' income from labour and the existing stock of K will be spread over more kids, so utility per kid (and utility per parent) will be lower. I think it depends on how much the marginal utility of consumption decreases.

In any case, suppose you are right. That would mean that Zero Population Growth would be an equilibrium, regardless of the initially level of the population, because all per capita variables would be unchanged if you doubled the number of kids, parents, and grandparents. If the Black Death killed off half the population, it would never recover to its original level. With land in the model I think we would get something more like a Malthusian model, with a long run steady state population, because Doubling all 3 generations would reduce output per person, because there is less land per worker.

Maybe we're misunderstanding each other. I said goes to zero not is zero. Black Death wipes out half the population, it grows back. But once it;s back, population growth stops. Of course this is with no exogenous productivity growth which is what your production function above implicitly assumes. Or are we confused between replacement fertility (zero population growth) and no kids (negative growth)?

As to the bigger question I'll get back to you, the answer doesn't seem straight forward. In any case, even without land, this is already a Malthusian model. Basically you need exogenous technological progress and possibility of capital accumulation to break out of Malthus (plus some more minor stuff). Either that or you assume preferences over children which give you a "Beckerian flip" in the population growth function in that if you ever get rich enough you start having fewer children.

notsneaky: "Black Death wipes out half the population, it grows back. But once it;s back, population growth stops."

I think I disagree. I can't see anything in the model that pins down the long run level of population. But I now realise that my "Black Death" thought experiment doesn't work, because it leaves the machines intact.

Suppose we are at steady state. Then a meteor shower kills half the kids, parents, and grandparents, and half the machines too. All the per-capita variables, and all the relative prices, would be unchanged. So each surviving parent would choose to have the same number of kids as before. So we are a new steady state.

With land in the model, if the meteor did not destroy the land, real per capita output would rise. The stock of land is exogenous, but capital is endogenous because it depreciates and can be built.

Hi Nick! If I might again interject with a nonrelated question what do you make of this quote from Warren Mosler on trade deficits?

"Imports are real benefits and exports are real
costs. Trade deficits directly improve our standard of
living. Jobs are lost because taxes are too high for a
given level of government spending, not because of
imports."

I see what you're saying. Without land, and as long as the saving rate is high enough the economy converges to a situation where K and L grow at same rate along a ray from origin (in a graph with K and L on the axis). If you cut both K and L by same %, you move down that ray but then resume growing along it, always keeping the same K/L ratio. It's not really that you're at a new steady state, it's that the steady state is in terms of the ratio, not individual variables. With the meteor, it's the same steady state really, you never left it (this I guess is a bit pedantic). Then immediately the economy will increase both its K and L to different levels, which is also the same steady state. In that case it's a little pointless to talk about level of population since it's always changing anyway.

This is actually how Solow originally presented his model in his 1953 paper if I remember correctly - with endogenous population, it was only later that people just made pop growth a constant.

If you add land to it however, then the economy converges to a constant level of capital and constant level of population (absent exogenous productivity growth) due to decreasing returns to scale (in the stuff that can actually change). There the long run level of population is tied down by the fact that in steady state population growth is zero (constant, with exo prod growth), just like the level of capital is tied down by the fact that net capital accumulation is zero. So long run steady state population is a function of some demographic parameters and the saving rate. I think that also means that here the "golden rule" of saving gets weird. Increasing saving rate will lower consumption today but also, because it will result in more people, it might lower consumption in the future. I haven't thought this part through completely though.

If a non-land destroying meteor hits this economy then, as you say, per capita output would rise and population would start increasing until it comes back to the same long run level.

I think I understood your previous comment to mean that in either situation the initial level of population matters - which it doesn't (land or no land) - but I think that was a misunderstanding on my part.

Scratch that last part about weird golden rule. Since with land this is a Malthusian model, steady state per capita income and consumption depend just on demographics and not on saving rate.

That actually does make it weird. It means you can cut your saving rate today, get more consumption, and then have exactly same consumption in steady state (just less people). I guess that's why you got to do this with OLG not Solow+land+population growth, to get rid of that weirdness.

Stepping back and thinking about the point of the post as whole, I got a couple further observations;

1. It seems like you're trying to flip that old Ricardian/Marxist argument that "capital is just stored up labor" on its head by saying "labor is also capital", because, with endogenous population, having children is just another way of transferring income or utility across time. And things which let you do that we call "capital"

2. The assumption of a Cobb-Douglas production function is not completely innocuous. Cobb-Douglas, or any production function where labor and capital are complements implicitly assumes that all factors of production are necessary for production. If your production function was L+K (or something where output can be positive with just K or just L) then it wouldn't be necessary for people to have children for capital to be productive in the future. This is the "we can just use robots" economy. Personally I tend to think that L and K being substitutes is sort of silly, even with robots, but, for example, Piketty spends A LOT of effort arguing that in fact they are substitutes (otherwise how do you explain the increase in capital's share) (this is one part where I think he's wrong). Anyway, if it's L+K or something like that, then there's no externality (not really)

3. But this also suggests that the whole thing can be flipped. If the production function is Cobb-Douglas, then you can just as easily argue that investing in capital, the K kind, has a externality, because otherwise, future workers would have no machines to work with. But we know just from out basic models, that that by itself does not create inefficiency. Capital owners get compensated for their investment and there's no efficiency. Unless we're talking about dynamic inefficiency...

4. But if population is endogenous, at least with land, that doesn't work either. In a Malthusian model, the growth rate of the economy is 0. Since real interest rates cannot be negative, we always have r>=g=0, so no dynamic inefficiency. We could put exogenous productivity growth in there to make g>0 but then r will just equal g, so once again no dynamic inefficiency.

5. Once you put a non accumulating factor like land and endogenous population growth in there, adding capital - as long as it is subject to diminishing returns - doesn't make much difference (I think). Might change some transitional dynamics, population will depend on the saving rate, but everything else is pretty much Malthusian. So might as well go with pure Malthus, since worrying about capital just complicates things (there might be/is a sort of "imbalance effect" in that in your initial situation the returns to capital and land might differ, so demand for one factor is zero. If you got a lot of capital you let it depreciate until its return is equal to the return on land, if you got little capital, you invest in it like crazy until its return is equal to the return on land, either way in steady state it does't matter)

6. You could make it more complicated by assuming that some people in the economy don't care about having children and some do. Assume that newborn people are chosen randomly to be one of the two types, rather than this preference being inherited (otherwise you'll converge to a "all breeder" economy or "no breeding" economy). Is there a positive externality that the breeders impose on the non-breeders, since the latter's capital wouldn't be productive without new workers? Yes, but it's priced correctly. Effectively, the proportion of breeders in the economy becomes a constant in the population growth equation, so up to scaling everything is the same as if they were all breeders or if "children just happened". This also means no inefficiency, and no possibility that some "social compact" where the non-breeders agree to have some children for the sake of making future land/capital more productive can be a Pareto improvement.

7. You don't need three ages in your OLG model. Just assume that children are born and instantaneously consume some resources (the cost of their rearing) and instantaneously turn into adults - it doesn't change anything. I think that's what Diamond explained to Samuelson, if I remember my HET correctly.

That is almost exactly what I tell my students. Imports are good, because foreigners use their scarce resources to produce goods, and we get to enjoy those goods, and exports are bad, because it's the opposite. But I then add that exports are a necessary evil, because foreigners will only accept so many little bits of paper for so long, in exchange for the goods they send us, unfortunately for us.

"Jobs are lost because taxes are too high for a
given level of government spending, not because of
imports."

I would change it to: jobs are lost because monetary policy is too tight, not because of imports. But tight money can cause exports to fall and imports to rise and that may be part of the mechanism why jobs are lost. But tight money would still cost jobs even if we restricted imports.

notsneaky: "Since with land this is a Malthusian model, steady state per capita income and consumption depend just on demographics and not on saving rate."

If you had land and capital, wouldn't it depend on both demographics and the saving rate? (But yes, with no capital only demographics would matter.)

1. "old Ricardian/Marxist argument that "capital is just stored up labor"

You could say that capital is stored up labour and land. But as any parent knows, kids are stored up labour and land too. Suppose we woke up and discovered all the history books are wrong, and actually the whole world of land, labour, machines, was created last night, by aliens, or by magic. Would it matter? What matters is the time structure of production looking forwards.

2. Yep, with C+I=L+K this would be a very different model. You would either invest in kids or invest in robots, but not both.

3. Hmmm. As D noted above, the externality isn't really an externality in the true sense, because it's a pecuniary externality. If I have more kids that increases the future R/W ratio, so it helps those who earn R and hurts those who earn W.

In many ways, this human capital and babies is a much bigger issue than ever as one reason why inflation can't reach 2% in the developed world is the slowdown of family formation. Japan was the first major nation to have a huge baby bust. And now Europe is following the Japanese example almost to "T" Some points:

1) According to Bryan Caplan, people did not have large families in the past because it was a retirement plan. (It was poor birth control first.) There were a huge number of children deaths and since the main capital was land, their net consumption/production was lower in 1800 than today.

2) The other reality today is people are not settling into careers until they are 30ish so they are economically wise to have kids until 32ish.

3) With large income inequality, families are spending a lot more time individual kids than in yesteryear. So 1950 family vs. today, spend the same time with kids but spent less per the ~4 kids of yesteryear.

4) Human kids 'production' is the one variable that effects the long run AD and AS curves. The problem with Japan is small families lower AD today and the effects of the AS are 20 years later.

5) Let us not think this baby bust is forever. With increased production the next several decades, we might see the return of the one income family. (It is already happening in the US and economist may call this trend the 'Home School Revolution') So more family production may occur and the costs of children are not as high. The richest and most functional nation, Norway, has an increasing rate today.

Actually, baby busts are separate from population busts. We see population busts in Japan and then Europe, and they are, indeed, related to baby busts. But you can have a baby bust without a population bust. There is a baby bust-without-population-bust that focusses my attention (I've been living with it for a while now!). It happened in Canada, where the fertility (replacement rate) fell from 3.8 in 1962 to 2.0 in 1972, while the population growth rate fell from 2.7 to 1.8%. That's that whole immigation thing here, which I'm bringing up in spite of the MEGO risk to underline the downside social risk of rapidly falling F(C+I,t) ["F" being the "good things" function that depends on time and C+I, which I decline to define] if immigration goes negative.

Nick's model allows for this as a steady state, but he throws up his hands. Such a population hardly merits study, as it will die off soon, anyway! Or, to put it another way, unsustainable situations will not be sustained, and so hardly need study as though they were permanent states of affairs!

As a historian of technology, though, I am not quite so sanguine. First, a pretence at pseudo-formal mathematical rigour. I am quite concerned with the idea that we write L and K as production functions dependent on some variable T, which we call "technology." Holding T constant means that we don't have to do dumb old calculus that ruins the model for us, and allows us to make some claim about the exogeneity of T, which perhaps exists in some space orthogonal ("Culture!") to our F(C+I,t). It strikes me as far more plausible that T is endogenous, itself a function of the "good things" function, T(F).

The general implication here --I'm really flying on intuition at the moment-- is that we end up with a positive feedback, with F constantly growing.

That's our intuition. It doesn't seem to be happening. Since L and K, like F, are functions of T(F), the math allows for the possiblity of a negative feedback. Throwing aside exogeneity, and my pretence to pseudo-formal mathematical rigour, the obvious explanation is that T is declining. It strikes me, and maybe it's just me, that a negative feedback loop causing a constant decline in the "good things" function, in which case clause (5) is whistling past the graveyard, and this is a hair-on-fire emergency for Canadians.

L and K are in the production function, they are not the production function. Y(T,K,L), where Y is output. If you generalize the idea of a "production function" though then with capital accumulation you could say that capital is produced with a production function which has old capital and old labor (and saving rare and depreciation) as arguments. Likewise if you go Malthusian, then new labor can be said to be "produced" with old capital and old labor.

The feedback from "other stuff" to endogenous technology T, is a subject of study in some models. In "learning by doing" models, technology depends on old capital. In Boserupian/Malthusian models, technology depends on old capital and old labor (and how closely to "subsistence income" these put you). In Michael Kremer's model, technology depends on the level of population. Etc. But to consider all these things, its useful to first work out just a baseline simple model.

" If I have more kids that increases the future R/W ratio, so it helps those who earn R and hurts those who earn W."

The thing that makes the whole thing efficient in a OLG model is exactly the fact that those who earn R and those who earn W are the same people (in the aggregate) just at different points in their life. Young people work and get w, which they use for consumption and to acquire capital/land, so last generations fertility hurts them. But then they grow up and own capital/land and that same fertility helps them. The only thing you can do in terms of welfare is to force the initial, generation 0 to have fewer kids which makes all subsequent generations better off. But there's no way to compensate that initial generation, so such a policy is not Pareto efficient.

Since notsneaky brought C+I = L+K up again and lent it some credibility, I'll post some more underinformed stuff:
So the robots simplification of the economy seems to be inaccurate ... Does this matter? To me what's interesting is that our economy is becoming more like the robots one and less like the model. Even if our incentives are still very like the incentives in the model, I want to know if a small but persistent erosion of those incentives can cause weird things to happen.
Or perhaps a better way to think about it is that the cost of creating one more unit of labor productivity through educating a human may be decreasing relative to the cost of creating a new human. So the production function can always stay multiplicative but generations can still decrease the population rationally. But I think the model requires these extra productive humans to consume just as much more at some point in their own retirement as their education allows them to produce?

> One thing I've been puzzling over, with my model, is whether introducing sex would change anything. If I replace "parents" with "mothers and fathers", the dynasties would keep crossing each other, but I'm not sure if anything else would change. The mother would care about her parents, and the father about his, for example, but if you model the couple as a cooperative equilibrium, I think things would come out much the same.

This only works is "mothers" and "fathers" are otherwise interchangeable, which greatly depends on culture. If hypothetically mothers provide the family income and fathers are seen as an indistinguishable commodity, then the relative bargaining power would be different. High-fitness mothers would be able to negotiate a more-than-even split of elder support to stiff the father's parents, whereas low-fitness mothers may be the opposite. My gut says that the competitive equilibrium with homogenous fathers and heterogeneous mothers would be that fathers' parents receive a society-wide fixed amount of support, but mothers' parents would benefit from unequal adult incomes.

Additionally, I think this model only makes sense in a semicompetitive format. If the model were fully competitive, then a family would be able to forego having children but contribute some of its own adult income to rearing others' children, in exchange for a portion of their own support obligations. If these obligations become marketable securities, then we're back to a sort of social pension.

Max, Nick: "Imports are real benefits and exports are real
costs. Trade deficits directly improve our standard of
living." (temporarily till you repay by a current account surplus he should add.) Like Nick, it's one thing that I try to make my students understand. Not esy to make them understanfd that a CA surplus is not "agood thing" but a debt payment...They listen too much to the commentariat. It doesn't help when sometimes, StatCan get a GDP number out and add "this will be revised downward as Import data will be available". This mlead them to think that imports are bad.
Business students are taught that exports pay for imports, which is true in the financial sense, not the economic sense.Anyone who reads european sources will always see references about "the need to earn foreigh exchange" or "dollar shortage " of the 40's-70's.
The more advanced may read about "those imports are ok because they are investment goods". No. Importing consumption goods are ok if they liberate resources for your own production of investment goods. It's the investment as such that is ok.
Germany do not understand how their "proof-of-their-virtuous-and-behavior" current account surplus is detrimental to their living standard.
I always tell students the fallacy of the "oil (or whatever)imports cost us $X billions, money that could stay here and create jobs instead of abroad." Making them understand that foreign goods are a gift (especially if you pay with your own fiat money) goes again their common sense and what they hear politicians and journos say daily.

I also tell them the day I finally truly understood that. It was during an International Economics cours. For years I had been going through the motions of comparative advantages. One day, I had a flash during the class. I finally saw how imports save you the ressources necessary for exports. They thought I was having a kind of seizure...

Jacques René Giguère: "I always tell students the fallacy of the "oil (or whatever)imports cost us $X billions, money that could stay here and create jobs instead of abroad."

Back in stagflation days there was the following story: Petrodollars went to Middle Eastern countries which, having no developed banking system of their own, sent them back to New York City banks, which then lent them at high interest rates to Latin American countries with poor credit ratings instead of lending them within the US, to Oklahoma farmers, for instance. Thus the US did not receive the benefit of increased money in circulation from the inflation caused by high oil prices.

Min: but those countries had to buy US goods.So the circuit is closed.Otherwise the Saudis are paid in monkey currency. So a competent CB should merely print money and give it to the oil producers. They didn't because the were concerned about "fighting inflation." They didn't understood that, at least temporarily, it was a real increase in the price of oil, a real not a monetary phenomenon. They raised interest rates, compounding the problem.

Adjustment problems arise however:
1) the mechanism isn't instantaneous. When the US consumers reduce their buying of let's say housing, there is a time lag before the Saudis order jet fighters.
2) the PSST is disturbed. People employed in the "housing" industry are not immediately and may not be forever employable and employed in the jet fighters sector.
Hope it's ok but busy and writing fast...